Lead-free Perovskites TlGeClxBr3-x (x=0,1,2,3) as Promising Materials for Solar Cell Application: a DFT Study

This study investigates the structural parameters and the electronic properties of cubic TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites to evaluate their potential as absorbers in perovskite solar cell devices. Density Functional Theory (DFT) embedded in the Quantum Espresso code was used to calculate these properties. The results revealed that the compounds have optimized lattice constants of 5.244 Å, 5.336 Å, 5.416 Å, and 5.501 Å, for TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites, respectively. In addition, the compounds are direct band gap (R→R) semiconductors with energy gap values of 0.847 eV, 0.683 eV, 0.556 eV, and 0.518 eV for the respective materials. It is important to note that the band gap of the perovskites reduces as a Cl− ion, two and three Cl− ions are replaced by a Br− ion, two and three Br− ions, respectively. The analysis of their projected density of states indicated that near the valence band maximum of the perovskites, Cl-3p and Br-4p states contributes the most to their total DOS. In contrast, the Ge-4p orbital is the most dominant state close to the conduction band minimum. Based on these energy gap values, the studied materials are promising candidates for lead-free perovskite solar cell devices, with TlGeBr3 projected to be more promising than the other three materials.


Introduction
Perovskites solar cells (PSCs) have become a promising 3 rd generation photovoltaic systems and have received considerable worldwide attention from the scientific community.The critical material in PSCs is the ABX3 perovskite that works as an active light-harvesting layer [1].Here, A and B are two cations while X is the anion.A wide range of perovskite materials have been studied both computationally and experimentally to investigate their promising applications in PSCs.
Among numerous perovskites studied, lead-based PSCs have the highest efficiency, comparable to conventional silicon-based solar cells.Recently, the efficiency of such PSCs has reached 25.8% [2], comparable to that of silicon-based solar cells with 26.6% efficiency [3].Silicon-perovskite tandem solar cells have been shown to have an efficiency of 29.80 % [4].However, perovskites in these PSCs contain toxic lead, preventing their large-scale fabrication [5].Therefore, a number of computational studies have been carried out to find lead-free perovskites with efficiency closely comparable to their lead-based counterparts.
Our previous study on TlGeF3 fluoro perovskite [37] showed that the material is a narrow bang gap semiconductor (1.52 eV) using the GGA approximation.This also agrees with the study of Zaman et al. [38], who reported a band gap of 1.59 eV for TlGeF3 using the GGA+U functional.These preliminary studies suggest that the material is a large bandgap semiconductor.Furthermore, it is expected that its isoelectronic compound of the form of TlGeCl3 and TlGeBr3 would have lower electronic band gaps as it was found in several studies that the replacement of halogen anions in perovskites by their counterparts with higher electronegativity leads to a decrease in the bandgap energy [39][40][41][42][43][44].Körbel et al. [45] reported the band gap energy of around 1.28 eV was found for TlGeBr3 using the more accurate HSE hybrid functional and that TlGeCl3 has a slightly larger electronic band gap.In these preliminary studies, the effect of varying the composition of the halide anions on the structure and the electrical properties of these perovskite compounds has not been investigated.
In the current work, the optimized structure and electrical properties of the cubic TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites are studied utilizing the Density Functional Theory (DFT), to evaluate their potential applications in optoelectronic devices, especially as absorbers in PSCs.The variation in the composition of the anions is predicted to affect the structural and electronic behavior of the perovskites.The DFT is used as it is widely known to be more powerful than some simple approximations, such as the semi-classical approximations and the simple matrix methods neglecting electron-electron correlation [46][47][48][49][50][51][52][53][54].The DFT has been widely applied to various materials and has proven accurate [55][56][57][58][59][60][61][62][63][64].

Method
Here, an ab-initio calculation using the DFT approach within the Quantum Espresso code [65] with the GGA-PBE functional [66] was implemented to study the structure and electrical properties of the cubic TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites.The Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach was used for the minimization procedure.The cut-off energy of 50 Ry was selected for the wave-function whereas that of 500 Ry was used for the charge density.In addition, K-points of 6x6x6 and 12x12x12 were used for the SCF and NSCF calculations, respectively.Meanwhile, the convergence threshold for the total energy was 10 -8 Ry.The crystal structure of the cubic TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3 belong to the space group #221 ‫3݉(‬ ത ݉). Figure 1 visualizes the structure of a unit cell of the TlGeCl3 perovskite, where Tl is sited at (0,0,0) and Ge occupies (0.5,0.5,0.5)position, whereas the Cl anions occupy the positions of (0.5,0,0.5), (0.5,0.5,0) and (0,0.5,0.5).For the TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites, the structure is the same, with one Cl anion, two and three Cl anions substituted with one Br anion, two and three Br anions, respectively.

Results and Discussion
This section presents and discusses the calculated structural and electronic properties of the cubic TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites.

Structural Properties
It is anticipated that the total energy of the compounds depends on their lattice constants.The total energy of the studied perovskites as a function of the lattice parameters of the cubic TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites is presented in Figure 2. As seen from the figure, the unit cell of the materials expands as a result of replacing Cl by Br ions.This is generally true for a large range of ABX3 perovskite compounds, where X anions are replaced by their counterparts with larger ionic radii [67][68][69][70][71][72].This is also observed for double perovskites [73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92].The optimized lattice constants of TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlG perovskites are 5.244 Å, 5.336 Å, 5.416 Å, and 5.501 Å, respectively (Table 1).Similar findings were reported for isoelectronic perovskites of the form CsPbClxBr3-x (x=0,1,2,3) lead-based perovskites [93], where the optimized lattice parameters of CsPbCl3 perovskite was found to be 5.728 Å.The authors [93] also observed that the lattice constants of the materials increase to 5.793 Å for CsPbCl2Br, 5.877 Å for CsPbClBr2, and 5.988 Å for CsPbBr3 perovskite.The increase in the lattice parameters impacts the materials' electrical properties, which will be presented and discussed further in the next section.The compounds' formation energy was computed, and the results are shown in Table 1.As the three compounds have negative formation energy, it can be inferred that they are chemically stable.Additionally, TlGeCl3 is projected to be the most stable perovskite in the current work, which is followed by TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites.This stability has also been predicted by our recent study on TlGeX3 [94], which is also true for other double perovskites [95].

Electronic properties
The electron density maps of TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites are plotted and illustrated in Figure 3.As evident from Figure 3, the Ge-X bonds (X = Cl or Br) are mainly covalent, whereas X is mostly ionic for all compounds.This is in line with previous studies on several thallium-based perovskites [37].Figure 3 also demonstrates that replacing Cl by Br did not significantly alter the electron density around Tl, Ge, and X ions, i.e., the Tl-X bonds remain mostly ionic, and Ge-X bonds remain mainly covalent.
The perovskites' electronic band diagrams were computed and the results are presented in Figure 4, along with the compounds "Total Density of States (TDOS)."At the same time, the numerical values of the energy gaps are depicted in Table 1.The overall characteristic of the diagram resembles that of several thallium-based fluoro perovskites reported in Ref [37], except that the forbidden gap found in the present study is smaller than that found in Ref [37].The studied materials possess direct semiconducting behavior (RAER) with energy gap values of 0.847 eV, 0.683 eV, 0.556 eV, and 0.518 eV for TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites, respectively.Substituting Cl with Br leads to a decrease in the bandgap of the perovskites while maintaining their direct type band gap behavior.The narrow and direct bandgaps of the perovskites clearly imply that they are potential for applications in optoelectronic devices which include perovskite solar cells.The slight decrease in the energy gap values as a result of changing a halogen anion with its counterparts with larger radii was also observed in other halide perovskites including CsPbClxBr3-x (x=0,1,2,3) perovskites [93], CsPbBr3−yIy (y = 0, 1, 2, 3) [96], CsPbCl3−yIy (y = 0, 1, 2, 3) [97], CsPbBr3-xYx(Y=I, Cl) [98], KGeI3-xBrx [99], MAPb (BrxI3-x)3 [100], and CsPbI3−xBrx (x = 0, 1, 2, 3) perovskites [101].As discussed in the previous section, replacing Cl with Br leads to an increase in the materials' optimized lattice constants, which is also accompanied by a decrease in their electronic band gaps.This can be attributed to the fact that the expansion of the unit cell of the materials results in the increase in the perovskites' bond length.This causes the electrons in the outermost shells of the perovskites to be less tightly bound to the atoms they belong to, and as a result, less energy is needed to make the electrons move more freely in the materials as conducting electrons.In other words, the energy gap of the compounds decreases [41].
The fact that the forbidden gaps of the perovskites become narrower when Br replacing Cl is due to the shift of the states, especially close to the valence band maximum, towards the Fermi level, as seen from the total DOS (TDOS) plots visualized in Figure 4.This reduces the size of the forbidden region between the conduction and valence bands of the perovskites.The decrease in the bandgaps suggests that the energy threshold of the materials' optic absorption would be shifted towards lower photon energy towards the visible light regions.This makes them more appropriate for application as absorbers in solar cell applications.This, of course, should be confirmed by investigating their optical properties.Moreover, the energy gaps of the materials can also be calculated using the Tauc-plot software using the UV-Vis absorption spectrum [102].To investigate the contribution of each state on the conduction and the valence bands of the studied compounds, the projected DOS (PDOS) have been plotted and illustrated in Figures 5a, 5b, 5c, and 5d for TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites, respectively.
Figures 5a and 5d indicate that near the valence band maximum of the perovskites, Cl-3p and Br-4p states contribute the most to the materials' total DOS.As one of the Cl anions is replaced by a Br anion in TlGeCl2Br (Figure 5b), the DOS of the Cl-3p state experiences a decrease following an increase in the Br-4p state, as expected.This is also apparent when two Cl anions are substituted with two Br anions in TlGeClBr2 (Figure 5c), where the Br-4p state becomes more dominant than the Cl-3p state near the valence band maximum.These results agree very well with the results reported by Islam et al. [93] for CsPbCl3-yBry (y = 0, 1, 2, and 3).The increase in the DOS of the Br-4p state is believed to push the top parts of the materials' valence bands towards the Fermi level, leading to a reduction in the perovskites' band gaps, as discussed in the previous section.Other studies on halide perovskites have also reported that in the region around the valence band maximum, the most dominant states are those of the halide anions [37; 96-97; 99-101].Meanwhile, near the conduction band minimum of the TlGeClxBr3-x (x=0,1,2,3) perovskites, the Ge-4p orbital is the most dominant state.In contrast, in a slightly higher energy within the materials' conduction band, Tl-6p state contributes the most to the total DOS of the studied compounds (see Figure 5).This is also consistent with other thallium-based perovskites including fluoro perovskites of the form TlBF3 [37], TlLF3 (L = Ca, Cd) [103], TlAF3 (A = Ge, Sn, Pb) [38], TlXF3 [104], and XBaF3 (X = Al and Tl) [105].

Conclusion
First-principles calculation based on DFT was performed to obtain the structural parameters and electrical properties of the cubic lead-free perovskites TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3.The materials were chemically stable and directly semiconducting with narrow band gaps.The perovskites' band gap values reduced when Cl anion was substituted by Br anion in the unit cell, with band gap energies (RAER) observed to be 0.847 eV, 0.683 eV, 0.556 eV, and 0.518 eV for TlGeCl3, TlGeCl2Br, TlGeClBr2, and TlGeBr3 perovskites, respectively.These narrow and direct band gaps strongly indicate that the materials are potential to be used in optoelectronic devices, including as absorbers in perovskite solar cells.Further studies are recommended to investigate the compounds' mechanical, optical, and thermoelectric properties.

Figure 1 .
Figure 1.The visualization of a unit cell of the cubic TlGeCl3.

Table 1 .
The lattice constants that have been optimized, the formation energy, and the energy band gaps of TlGeClxBr3-x (x=0,1,2,3) lead-free perovskites.